Answer
$x=1.5,11.5$
Work Step by Step
When taking the square root of a number, you get a positive and a negative answer.
$2.5(x-6.5)^2-20=42.5$
$2.5(x-6.5)^2=62.5$
$(x-6.5)^2=25$
$x-6.5=5$
$x=11.5$
or
$x-6.5=-5$
$x=1.5$.
So
$x=1.5,11.5$.